{"paper":{"title":"Trees and asymptotic developments for fractional stochastic differential equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas Neuenkirch, Andreas R\\\"o{\\ss}ler, Ivan Nourdin (PMA), Samy Tindel (IECN)","submitted_at":"2006-11-10T10:44:33Z","abstract_excerpt":"In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H>1/3. After solving this equation in a rather elementary way, following the approach of Gubinelli, we show how to obtain an expansion for E[f(X\\_t)] in terms of t, where X denotes the solution to the SDE and f:R^n->R is a regular function. With respect to the work by Baudoin and Coutin, where the same kind of problem is considered, we try an improvement in three different directions: we are able to take a drift into account in the equation, we parametrize our "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611306","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}